Next month’s Notices of the AMS has an essay by Freeman Dyson entitled Frogs and Birds, which was written for his planned Einstein Public Lecture. In it, he divides mathematicians up into two species: birds, who “fly high in the air and survey broad vistas” (i.e. seek abstraction, unification and generalization), and frogs, who “see only the flowers that grow nearby” (i.e. study the details of specific examples).

Dyson himself is resolutely a frog, but writes that “many of my best friends are birds”, and argues that both birds and frogs are needed to do justice to the breadth and depth of the subject of mathematics. Frog that he is, his essay covers a variety of quite different special topics that have drawn his attention, linked together only weakly by the bird/frog theme. These include a discussion of the roles of complex numbers and linearity in quantum mechanics, a proposed idea about how to attack the Riemann hypothesis (try and enumerate 1d-quasicrystals, since the zeros of the zeta function have this structure), and a collection of profiles and anecdotes about various mathematicians and physicists (Besicovitch, Weyl, Yang, Manin, von Neumann).

Personally I suppose I fit well into Dyson’s bird category, but among the best mathematicians that I know, the frog/bird distinction is often unclear. Many of them make their reputation by proving rather abstract and general theorems, but these proofs are often the result of a huge amount of detailed investigation of examples. I agree with Dyson that both points of view are needed, and see the most successful cases of progress in mathematics coming from mathematicians who avoid the temptation to fly too high into arid abstraction, or sink too deep into irrelevant detail.

Dyson includes a long section on string theory, which I’ll include here:

I would like to say a few words about string theory. Few words, because I know very little about string theory. I never took the trouble to learn the subject or to work on it myself. But when I am at home at the Institute for Advanced Study in Princeton, I am surrounded by string theorists, and I sometimes listen to their conversations. Occasionally I understand a little of what they are saying. Three things are clear. First, what they are doing is first-rate mathematics. The leading pure mathematicians, people like Michael Atiyah and Isadore Singer, love it. It has opened up a whole new branch of mathematics, with new ideas and new problems. Most remarkably, it gave the mathematicians new methods to solve old problems that were previously unsolvable. Second, the string theorists think of themselves as physicists rather than mathematicians. They believe that their theory describes something real in the physical world. And third, there is not yet any proof that the theory is relevant to physics. The theory is not yet testable by experiment. The theory remains in a world of its own, detached from the rest of physics. String theorists make strenuous efforts to deduce consequences of the theory that might be testable in the real world, so far without success.

My colleagues Ed Witten and Juan Maldacena and others who created string theory are birds, flying high and seeing grand visions of distant ranges of mountains. The thousands of humbler practitioners of string theory in universities around the world are frogs, exploring fine details of the mathematical structures that birds first saw on the horizon. My anxieties about string theory are sociological rather than scientific. It is a glorious thing to be one of the first thousand string theorists, discovering new connections and pioneering new methods. It is not so glorious to be one of the second thousand or one of the tenth thousand. There are now about ten thousand string theorists scattered around the world. This is a dangerous situation for the tenth thousand and perhaps also for the second thousand. It may happen unpredictably that the fashion changes and string theory becomes unfashionable. Then it could happen that nine thousand string theorists lose their jobs. They have been trained in a narrow specialty, and they may be unemployable in other fields of science.

Why are so many young people attracted to string theory? The attraction is partly intellectual. String theory is daring and mathematically elegant. But the attraction is also sociological. String theory is attractive because it offers jobs. And why are so many jobs offered in string theory? Because string theory is cheap. If you are the chairperson of a physics department in a remote place without much money, you cannot afford to build a modern laboratory to do experimental physics, but you can afford to hire a couple of string theorists. So you offer a couple of jobs in string theory, and you have a modern physics department. The temptations are strong for the chairperson to offer such jobs and for the young people to accept them. This is a hazardous situation for the young people and also for the future of science. I am not saying that we should discourage young people from working in string theory if they find it exciting. I am saying that we should offer them alternatives, so that they are not pushed into string theory by economic necessity.

Finally, I give you my own guess for the future of string theory. My guess is probably wrong. I have no illusion that I can predict the future. I tell you my guess, just to give you something to think about. I consider it unlikely that string theory will turn out to be either totally successful or totally useless. By totally successful I mean that it is a complete theory of physics, explaining all the details of particles and their interactions. By totally useless I mean that it remains a beautiful piece of pure mathematics. My guess is that string theory will end somewhere between complete success and failure. I guess that it will be like the theory of Lie groups, which Sophus Lie created in the nineteenth century as a mathematical framework for classical physics. So long as physics remained classical, Lie groups remained a failure. They were a solution looking for a problem. But then, fifty years later, the quantum revolution transformed physics, and Lie algebras found their proper place. They became the key to understanding the central role of symmetries in the quantum world. I expect that fifty or a hundred years from now another revolution in physics will happen, introducing new concepts of which we now have no inkling, and the new concepts will give string theory a new meaning. After that, string theory will suddenly find its proper place in the universe, making testable statements about the real world. I warn you that this guess about the future is probably wrong. It has the virtue of being falsifiable, which according to Karl Popper is the hallmark of a scientific statement. It may be demolished tomorrow by some discovery coming out of the Large Hadron Collider in Geneva.

I don’t know where Dyson got the estimate of ten thousand string theorists; my own estimate would be more like one to two thousand (with the number strongly dependent on how you decide who is a “string theorist”). The large yearly Strings200X conferences that bring together a sizable fraction of active string theory community tend to draw roughly 500 people.

The Princeton-centric assumption that there are lots of string theory jobs embedded in his question “And why are so many jobs offered in string theory?” is quite problematic, as any young string theorist on the job market could explain to him. There actually aren’t a lot of string theory jobs out there, and a lot of Ph.D.s in the subject being produced, leading to a lot of ex-string theorists now working in the financial industry and elsewhere. These days, if you are going to choose your field based on where the jobs are, you become an LHC phenomenologist or a cosmologist. If you want to be a string theorist, you better be a string phenomenologist or a string cosmologist. Also rather unrealistic is Dyson’s “it could happen that nine thousand string theorists lose their jobs”, due to tenure in the academic system. Even if a consensus develops over the next few years that string theory was all a big mistake, twenty years from now there will still be a cadre of (older) people working in the field.

Dyson’s idea, that 50-100 years from now, a new revolution in physics will show how string theory fits in may be right. It also may be that this has already happened, as much of the field has moved into the study of gauge-string dualities, where string theory provides a useful approximation for strongly coupled systems, and the idea that it unifies particle physics is falling by the wayside.

Dear Peter,

Thanks for pointing out that nice piece of an essay. As a stringy person myself I would however disagree with Dyson saying that string theorists are too narrowly trained to be useful in other parts of science. People who enter a PhD program in string theory in a reknown place (need not to be Princeton) are good physicists already from their undergrad time, as the students normally interested in string theory are interested in deep questions of physics in general, and for this they need to understand the basics of physics to a good extend, which in turn means they have done their homework already as an undergrad. This is at least my experience. So they are well-trained physicists, and can in principle with some preparation time work in any field of theoretical physics. Also, for understanding the implications of string theory one needs to be well-trained in nearly all subjects of basic theoretical physics, which there are mathematical methods, classical and quantum field theory, statistical physics and gravity/GR. The average string theorist is well-trained in all these subjects. What makes the change of subject away from string theory even to closely related areas like “quantum gravity” (for the purpose here just summarizing all attempts to quantum gravity except string theory), classical gravity or pure cosmology is, in my experience, rather the attitude of other communities towards string theory, which is often full of prejudices originating from hearsay, the failure to understand even the stringy basics and the dissatisfaction thus created. Its often a one-way road: String theorists understand what other people are doing, but the other people dont understand string theory. With such a structure, it is nearly impossible to change for a postdoc in a different field, as everybody takes only the people whose work he knows and understands. This is partly also true in string theory, of course.

Another remark: Not only string theory is cheap, whole theoretical physics is, if you dont need supercomputers. So poorer universities can higher also other people…

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Thanks for Dyson’s interesting article, Peter. The essay was overall balanced I think, so I will state a few issues with which I disagree.

1. People don’t go into string theory for jobs. I was very sternly warned that going into string theory is dangerous, careerwise, and no string theorist I know had any illusions about it when they got into it either. I suspect that Dyson is forgetting why he went into mathematics and theoretical physics back when he was an excitable young man, but thats just my guess.

2. While agreeing with the possibility that string theory might be only part of the full picture, I would like to point out that since we don’t have the benefit of hindsight, the only working strategy we have available for progress NOW is to push our current theories to their limits. Revolutions, almost by definition, cannot appear on demand. To give an example: It took almost twenty years of work on seemingly pointless things like gauged supergravities, many dimensions, superconformal algebras, large N gauge theories etc. before it all finally came together in gauge-gravity duality.

3. String theory being superspecialized is also a weird claim. One of the challenges that an aspiring string theorist faces is in fact the ridiculous amount of physics and math they have to learn. I think the real problem is not that string theory is superspecialized, but that some string theorists are superspecialized to one subfield or even to one problem. But this is not just a feature of the string theory community …

Rene,

I agree that Dyson’s explanation that string theorists get hired because they are cheap doesn’t explain anything, since they are no more or less expensive than other theorists.

As for the somebody’s point that string theorists don’t go into the subject because job prospects are good, that’s certainly right, more so now than ever. The question though is a relative one. The job situation in theoretical physics in general has been terrible for a long time. If you decide you want to try for a career as a theoretical physicist, despite the odds, does going into string theory maximize your chances? I think now someone who wants to maximize their chances is more likely to go into phenomenology or cosmology. But if your interest is in fundamental, more mathematical and formal approaches, you still may not have any real alternative to string theory. The job situation for string theorists is bad, but jobs in formal theory that is not string theory are pretty much non-existent in physics departments, at least in the US.

My impression of the background of string theorists is that it varies widely. Some do actually know a lot of physics and mathematics, and have a good chance of changing fields if they want to. Others don’t, and suffer from the disability of not knowing how little they know, making it highly unlikely that they’ll ever be able to do what it takes to move to another field.

I love Dyson’s paper. To me, though, the strong point is the detailed and insightful History of transdisciplinary unifiers in Mathematics, and the surprise that this is useful in understanding Physics. I feel that Context trumps Content here. But I agree with the comments that we’ll have a batter idea in 50-100 years what this was all about, in the late 20th century. If I’m very lucky, I’ll be here in 50 years (aged 107). Nobody yet has been 157, so I’m not going to invest much effort in what might be known in 100 years.

Dear Peter,

I have to disagree on the job situation. I just applied for my first postdoc, got some offers, but it was a very competitive thing. Nowadays string community in Europe and the US/Canada is very competitive on the postdoc level already, not to speak about tenure track. I have a little bit of insight into other fields of theoretical physics, where people are handled around to their next postdoc until they are old enough for tenure track. They do not have to go through all the pain of applying worldwide without knowing whether they should get a job at all. Long story short: In my opinion the job market in the string community is more competitive and less connection-driven than in other fields of theoretical physics.

But feel free to disagree.

Best, Rene.

Rene,

I don’t disagree at all that the job market for string theorists is now highly competitive.

I don’t really understand why he thinks lie groups are a failure for classical physics, or why the analogy makes much sense =/

Dyson’s 50-100 years guess is for a revolution is identical to the guess in his 1981 essay Unfashionable Pursuits:

‘… At any particular moment in the history of science, the most important and fruitful ideas are often lying dormant merely because they are unfashionable. Especially in mathematical physics, there is commonly a lag of fifty or a hundred years between the conception of a new idea and its emergence into the maintsream of scientific thought. If this is the time scale of fundamental advance, it follows that anybody doing fundamental work in mathematical physics is almost certain to be unfashionable. …’

– Dyson’s 1981 essay, Unfashionable Pursuits

The number 10000 may come from “Brief History of Time”. Somewhere it is written that 10000 people are doing string theory world wide, at least that what I remember.

About the job situation, it is really bad in string theory. There should not be any question about that. But the situation was probably a little different in late nineties.

Peter,

You write “Personally I suppose I fit well into Dysonâ€™s bird category” which makes me wonder, which fields of mathematics/physics did you unify, generalize or abstracted to a higher level? By looking at your record on spires, it’s not at all clear what you mean. It seems to me your research has been pretty focused on a single topic, topological aspects of non-abelian gauge theories, which to me seems to fit the frog category.

Your thoughts?

Thanks for reading,

Grant

Grant,

My early research was on topological effects in lattice gauge theory, but my general area of interest is trying to find new ways of understanding the underlying structure of the standard model using modern mathematics and representation theory. One of my problems in life is that my bird-like tendencies have led me to spend a large fraction of my time flying around at too high altitude trying to learn about different kinds of mathematical structures that might be useful, instead of getting down to ground and working out details and publishing.

The current ideas about BRST that I’m working on and trying to get down to detail with involve algebraic ideas that are very far from the topological and geometrical ideas that I started with. It has taken me a long time to start to appreciate the algebraic approach.

In any case, I recognize my tendencies (if not my accomplishments..) in Dyson’s description of birds, find his description of “frogs” much more alien (e.g. when he says that he had no interest in the relations between number theory and QM that were pointed out to him)

Peter,

I’m not sure that I follow Dyson’s analogy between Lie groups and string theory. As I understand it, Lie was trying to create a Galois theory for differential equations. The ‘disappointment’ to which Dyson refers stemmed from his perception of a lack of recognition for his work, and not so much from a lack of applications.

I also don’t understand his description of Lie groups as a failure in classical physics, although admittedly it took until the 1940s before Lie’s ideas started to be applied systematically (to hydrodynamics). (Refer the CRC Handbook of Lie Group Analysis of Differential Equations for an overview of more recent applications.)

I think that it may be more accurate to say that for both classical and quantum mechanics, Lie’s ideas needed further development and refinement. For example, the theory of representations of Lie algebras (to which Dyson refers to as natural language of particle physics) was a considerable advance from Lie’s concept of ‘infinitesimal groups’. As ‘Not Even Wrong’ describes, it took a considerable period for these ideas to be understood and accepted.

If there is indeed an analogy for string theory, perhaps it is that the necessary tool or tools for progress already exist in contemporary mathematics, but they may also need further development. And it may not be at all obvious at the outset that these tools are in fact useful at all.

A related but somewhat different kind of division can be found in the essay Two Cultures of Mathematics by W.T. Gowers.